I don't recall ever being bitten by a RES, at least not that I'm aware of. But, they will likely not provide enough forage on their own for a population of hungry LMB. I wonder if the combination of RES and Tilapia would enable year-round support of the LMB? One forage during the warmer months, another for the colder periods.
If you're willing to feed, you might try RES and HSB together. If the RES get carried away, you could add a few single sex LMB to thin them out.